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Results tagged with hypergeometric-functions
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Hypergeometric functions are the analytic functions defined by Taylor expansions of the shape $\sum_{n \geq 0} a_n x^n$, where $a_{n+1}/a_n$ is a rational function of $n$. This general family of functions encompasses many classical functions. The hypergeometric functions play an important role in many parts of mathematics.
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Reflection formula for the ${}_2\!F_1$ hypergeometric function of a matrix argument
According to my implementation of the hypergeometric function of a matrix argument, the so-called "Reflection formula" for ${}_2\!F_1$ given on DMLF (formula 35.7.8) is not true.
On the Wikipedia art …
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Does the hypergeometric function of a matrix argument depend on $\alpha$ for a $1\times 1$ m...
I already posted this question on maths.SE but got no answer.
The hypergeometric function of a matrix argument has form
$$
{}_pF_q^{(\alpha)}(a_1, \ldots, a_p; b_1, \ldots, b_q;X) =
\sum_{k=0}^\inft …
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Why do we define the hypergeometric function of a matrix argument for symmetric matrices only?
The hypergeometric function of a matrix argument has form
$$
{}_pF_q^{(\alpha)}(a_1, \ldots, a_p; b_1, \ldots, b_q;X) =
\sum_{k=0}^\infty\sum_{\kappa\vdash k} c^{(\alpha)}_{a,b} J^{(\alpha)}_\kappa(X …
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Integrals involving the Tricomi hypergeometric function
I am looking for a reference for the two following equalities involving the Tricomi function $U$ and the Meijer function $G$. I have found these formulas on the website http://functions.wolfram.com/, …
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answer
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integral involving hypergeometric function of matrix argument
This conjecture comes from an observation on simulations of the matrix variate noncentral Beta distribution (similar to this observation, but I open a new question because yet I'm not sure it is exact …
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